%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:45:04 AM UTC 2026
% Result : Unsatisfiable 7.99s 3.55s
% Output : Refutation 8.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 1
% Syntax : Number of formulae : 61 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 440 ( 67 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 320 ( 75 ~; 67 |; 9 &; 169 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $o > $o ).
thf(g_decl,type,
g: $o > $o ).
thf(x_decl,type,
x: $o ).
thf(y_decl,type,
y: $o ).
thf(1,axiom,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',3) ).
thf(2,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(cnf,[status(esa)],[2]) ).
thf(6,plain,
( ( g @ y )
= x ),
inference(cnfConj,[status(thm)],[3]) ).
thf(10,plain,
( ( g @ y )
= x ),
inference(lifteq,[status(thm)],[6]) ).
thf(7,plain,
( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ),
inference(cnfConj,[status(thm)],[3]) ).
thf(11,plain,
( ( g @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(5,plain,
( ( g @ x )
= y ),
inference(cnfConj,[status(thm)],[3]) ).
thf(9,plain,
( ( g @ x )
= y ),
inference(lifteq,[status(thm)],[5]) ).
thf(24,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( g @ ( f @ x ) )
!= ( g @ x ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(28,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[24]) ).
thf(27,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( g @ ( f @ x ) )
!= ( g @ y ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(30,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( f @ x )
!= y ) ),
inference(simp,[status(thm)],[27]) ).
thf(133,plain,
( ( ( f @ x )
!= y )
| ( y = x )
| ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ ( f @ ( f @ x ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,28]) ).
thf(134,plain,
( ( ( f @ x )
!= y )
| ( y = x )
| ( ( f @ x )
!= x ) ),
inference(pattern_uni,[status(thm)],[133:[]]) ).
thf(4,plain,
x != y,
inference(cnfConj,[status(thm)],[3]) ).
thf(8,plain,
y != x,
inference(lifteq,[status(thm)],[4]) ).
thf(212,plain,
( ( ( f @ x )
!= y )
| ( ( f @ x )
!= x ) ),
inference(simplifyReflect,[status(thm)],[134,8]) ).
thf(217,plain,
( ( ( f @ x )
!= x )
| ( y != y )
| ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[28,212]) ).
thf(218,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(225,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[218]) ).
thf(244,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) )
| ( x != x ) ),
inference(eqfactor_ordered,[status(thm)],[225]) ).
thf(252,plain,
( ( ( f @ x )
!= x )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[244]) ).
thf(257,plain,
( ( f @ x )
!= x ),
inference(simp,[status(thm)],[252]) ).
thf(259,plain,
( ( f @ x )
| x ),
inference(bool_ext,[status(thm)],[257]) ).
thf(13,plain,
( y
| x ),
inference(bool_ext,[status(thm)],[8]) ).
thf(33,plain,
( x
| ( ( g @ $true )
= x )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[13,10]) ).
thf(34,plain,
( x
| ( ( g @ $true )
= x ) ),
inference(pattern_uni,[status(thm)],[33:[]]) ).
thf(43,plain,
( x
| ~ ( g @ $true )
| x ),
inference(bool_ext,[status(thm)],[34]) ).
thf(57,plain,
( x
| ~ ( g @ $true ) ),
inference(simp,[status(thm)],[43]) ).
thf(63,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ( ( g @ ( f @ x ) )
!= ( g @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[11,57]) ).
thf(65,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[63]) ).
thf(68,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[65]) ).
thf(70,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[68]) ).
thf(72,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) )
| x ),
inference(bool_ext,[status(thm)],[70]) ).
thf(73,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(83,plain,
( x
| ~ ( f @ x )
| x
| ~ ( f @ $true )
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,65]) ).
thf(84,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[84:[]]) ).
thf(105,plain,
( x
| ~ ( f @ x )
| x
| ~ ( f @ x )
| ~ $true
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[73,85]) ).
thf(106,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(109,plain,
( x
| ~ ( f @ x )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[106]) ).
thf(112,plain,
( x
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[109]) ).
thf(273,plain,
( x
| x
| ~ $true
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[259,112]) ).
thf(274,plain,
( x
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
x,
inference(pattern_uni,[status(thm)],[274:[]]) ).
thf(297,plain,
g @ y,
inference(rewrite,[status(thm)],[10,275]) ).
thf(12,plain,
( ~ y
| ~ x ),
inference(bool_ext,[status(thm)],[8]) ).
thf(300,plain,
( ~ y
| ~ $true ),
inference(rewrite,[status(thm)],[12,275]) ).
thf(301,plain,
~ y,
inference(simp,[status(thm)],[300]) ).
thf(309,plain,
g @ $false,
inference(rewrite,[status(thm)],[297,301]) ).
thf(302,plain,
( ( g @ ( f @ $true ) )
= ( f @ ( f @ ( f @ $true ) ) ) ),
inference(rewrite,[status(thm)],[11,275]) ).
thf(298,plain,
~ ( f @ $true ),
inference(rewrite,[status(thm)],[257,275]) ).
thf(323,plain,
( ( g @ $false )
= ( f @ ( f @ $false ) ) ),
inference(rewrite,[status(thm)],[302,298]) ).
thf(324,plain,
f @ ( f @ $false ),
inference(rewrite,[status(thm)],[309,323]) ).
thf(331,plain,
( ~ $true
| ( ( f @ ( f @ $false ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[324,298]) ).
thf(332,plain,
( ( f @ ( f @ $false ) )
!= ( f @ $true ) ),
inference(simp,[status(thm)],[331]) ).
thf(338,plain,
~ ( f @ $false ),
inference(simp,[status(thm)],[332]) ).
thf(342,plain,
f @ $false,
inference(rewrite,[status(thm)],[324,338]) ).
thf(345,plain,
$false,
inference(rewrite,[status(thm)],[342,338]) ).
thf(346,plain,
$false,
inference(simp,[status(thm)],[345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.24 % Computer : n014.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 16:24:00 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.12/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.17 % [INFO] Parsing done (192ms).
% 1.61/1.19 % [INFO] Running in sequential loop mode.
% 2.35/1.62 % [INFO] eprover registered as external prover.
% 2.35/1.63 % [INFO] Scanning for conjecture ...
% 2.35/1.68 % [INFO] 1 axioms and no conjecture found.
% 2.61/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.61/1.71 % [INFO] Type checking passed.
% 2.61/1.72 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.99/3.54 % [INFO] Killing All external provers ...
% 7.99/3.54 % Time passed: 3068ms (effective reasoning time: 2341ms)
% 7.99/3.54 % Axioms used in derivation (1): 3
% 7.99/3.54 % No. of inferences in proof: 61
% 7.99/3.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3068 ms resp. 2341 ms w/o parsing
% 8.43/3.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.43/3.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------